Discrete Globalised Dual Heuristic Dynamic Programming in Control of the Two-Wheeled Mobile Robot

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td align="left">Control algorithm</td><td align="center">PD</td><td align="center">HDP</td><td align="center">GDHP</td><td align="center">DHP</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td align="left"><span style="width: 25.3723ptpx;"><svg height="9.61891pt" id="M273" style="vertical-align:-3.40875pt" version="1.1" viewbox="-0.0498162 -6.21016 25.3723 9.61891" width="25.3723pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M352 391C352 416 319 448 267 448C236 448 173 423 147 400C107 364 96 332 96 304C96 248 143 210 193 181C241 153 258 124 258 100C258 72 232 38 184 38C151 38 107 66 81 108C77 114 64 116 55 111C34 99 23 84 23 65C23 29 81 -12 134 -12C220 -12 325 61 325 141C325 184 297 215 234 256C194 282 161 309 161 346C161 380 188 401 217 401C255 401 279 380 301 353C308 344 313 341 325 347C341 355 352 371 352 391Z" id="g113-116"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="375" vert-adv-y="375"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,5.013,3.264)"><path d="M797 0V26C739 32 732 36 732 103V296C732 394 682 449 605 449C576 449 550 437 529 423C504 407 475 389 446 366C425 418 382 449 334 449C303 449 279 437 253 421C222 403 201 385 180 371V452C135 432 85 419 41 411V388C99 379 102 374 102 310V103C102 38 93 32 27 26V0H238V26C189 32 180 38 180 103V338C210 363 250 390 289 390C351 390 377 348 377 275V103C377 37 368 32 306 26V0H520V26C465 32 456 38 456 101V296C456 314 455 326 453 338C491 369 529 390 565 390C628 390 653 345 653 274V107C653 36 642 32 583 26V0H797Z" id="g190-110"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="819" vert-adv-y="819"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,12.751,3.264)"><path d="M433 39L423 65C413 59 399 54 387 54C370 54 352 69 352 114V299C352 352 342 392 307 422C285 440 255 449 225 449C168 437 102 399 75 379C56 365 44 353 44 339C44 315 69 296 87 296C101 296 111 303 116 319C124 349 133 371 145 385C156 397 171 404 190 404C241 404 275 364 275 291V274C253 256 180 229 120 209C65 190 39 159 39 110C39 47 88 -12 159 -12C189 -12 237 25 277 52C282 35 288 21 301 8C312 -3 333 -12 348 -12L433 39ZM275 84C256 65 221 48 195 48C164 48 124 73 124 124C124 161 146 180 185 198C206 208 254 229 275 240V84Z" id="g190-98"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="439" vert-adv-y="439"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,16.743,3.264)"><path d="M478 437H300V411C357 404 363 393 347 345C325 280 293 190 258 107C229 178 188 284 163 354C147 397 149 405 203 411V437H-2V411C52 403 59 396 82 339C130 222 176 109 220 -11H248C304 138 356 261 390 336C417 395 425 404 478 411V437Z" id="g190-119"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="463" vert-adv-y="463"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,21.163,3.264)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z" id="g190-115"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="371" vert-adv-y="371"></glyph.data></g></svg></span></td><td align="center">4.06</td><td align="center">2.24</td><td align="center">1.66</td><td align="center">1.52</td></tr><tr><td align="left"><span style="width: 17.8086ptpx;"><svg height="9.61891pt" id="M274" style="vertical-align:-3.40875pt" version="1.1" viewbox="-0.0498162 -6.21016 17.8086 9.61891" width="17.8086pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0135,0,0,-0.0135,0,0)"><path d="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z" id="g113-247"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="410" vert-adv-y="410"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,5.216,3.264)"><path d="M433 39L423 65C413 59 399 54 387 54C370 54 352 69 352 114V299C352 352 342 392 307 422C285 440 255 449 225 449C168 437 102 399 75 379C56 365 44 353 44 339C44 315 69 296 87 296C101 296 111 303 116 319C124 349 133 371 145 385C156 397 171 404 190 404C241 404 275 364 275 291V274C253 256 180 229 120 209C65 190 39 159 39 110C39 47 88 -12 159 -12C189 -12 237 25 277 52C282 35 288 21 301 8C312 -3 333 -12 348 -12L433 39ZM275 84C256 65 221 48 195 48C164 48 124 73 124 124C124 161 146 180 185 198C206 208 254 229 275 240V84Z" id="g190-98"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="439" vert-adv-y="439"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,9.208,3.264)"><path d="M478 437H300V411C357 404 363 393 347 345C325 280 293 190 258 107C229 178 188 284 163 354C147 397 149 405 203 411V437H-2V411C52 403 59 396 82 339C130 222 176 109 220 -11H248C304 138 356 261 390 336C417 395 425 404 478 411V437Z" id="g190-119"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="463" vert-adv-y="463"></glyph.data></g><g transform="matrix(.0095,0,0,-0.0095,13.628,3.264)"><path d="M181 342V451C133 431 89 419 40 411V388C98 381 102 377 102 311V104C102 38 95 32 33 26V0H263V26C186 32 181 38 181 104V287C203 343 235 372 261 372C277 372 289 366 304 352C310 346 318 345 330 350C349 359 362 379 362 399C362 422 338 449 304 449C256 449 213 393 183 342H181Z" id="g190-115"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="371" vert-adv-y="371"></glyph.data></g></svg></span></td><td align="center">1.99</td><td align="center">0.42</td><td align="center">0.32</td><td align="center">0.24</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab1

Table 1

Table 1: Discrete Globalised Dual Heuristic Dynamic Programming in Control of the Two-Wheeled Mobile Robot 